





import tempfile

import torch

from diffusers import (
    DEISMultistepScheduler,
    DPMSolverMultistepScheduler,
    DPMSolverSinglestepScheduler,
    UniPCMultistepScheduler,
)

from .test_schedulers import SchedulerCommonTest




class 			__UpperCamelCase    (							A__    ):
     __A	:  List[str]							  =   (UniPCMultistepScheduler,)
     __A	:  List[str]							  =   (("""num_inference_steps""", 25),)





     def 		UpperCamelCase(     self				,							**_UpperCamelCase					):
        _UpperCAmelCase           =   {
            '''num_train_timesteps''': 1000,
            '''beta_start''': 0.0001,
            '''beta_end''': 0.02,
            '''beta_schedule''': '''linear''',
            '''solver_order''': 2,
            '''solver_type''': '''bh2''',
        }

        config.update(**_UpperCamelCase					)
        return config





     def 		UpperCamelCase(     self				,							_UpperCamelCase=0				,							**_UpperCamelCase					):
        _UpperCAmelCase           =   dict(self.forward_default_kwargs					)
        _UpperCAmelCase           =   kwargs.pop('''num_inference_steps'''				,							_UpperCamelCase					)
        _UpperCAmelCase           =   self.dummy_sample
        _UpperCAmelCase           =   0.1 * sample
        _UpperCAmelCase           =   [residual + 0.2, residual + 0.15, residual + 0.10]

        for scheduler_class in self.scheduler_classes:
           _UpperCAmelCase           =   self.get_scheduler_config(**_UpperCamelCase					)
           _UpperCAmelCase           =   scheduler_class(**_UpperCamelCase					)
           scheduler.set_timesteps(_UpperCamelCase					)
           # copy over dummy past residuals
           _UpperCAmelCase           =   dummy_past_residuals[: scheduler.config.solver_order]

           with tempfile.TemporaryDirectory() as tmpdirname:
              scheduler.save_config(_UpperCamelCase					)
              _UpperCAmelCase           =   scheduler_class.from_pretrained(_UpperCamelCase					)
              new_scheduler.set_timesteps(_UpperCamelCase					)
              # copy over dummy past residuals
              _UpperCAmelCase           =   dummy_past_residuals[: new_scheduler.config.solver_order]

           _UpperCAmelCase       ,      _UpperCAmelCase           =   sample, sample
           for t in range(_UpperCamelCase				,							time_step + scheduler.config.solver_order + 1					):
              _UpperCAmelCase           =   scheduler.step(_UpperCamelCase				,							_UpperCamelCase				,							_UpperCamelCase				,							**_UpperCamelCase					).prev_sample
              _UpperCAmelCase           =   new_scheduler.step(_UpperCamelCase				,							_UpperCamelCase				,							_UpperCamelCase				,							**_UpperCamelCase					).prev_sample

              assert torch.sum(torch.abs(output - new_output					)					) < 1e-5, "Scheduler outputs are not identical"





     def 		UpperCamelCase(     self				,							_UpperCamelCase=0				,							**_UpperCamelCase					):
        _UpperCAmelCase           =   dict(self.forward_default_kwargs					)
        _UpperCAmelCase           =   kwargs.pop('''num_inference_steps'''				,							_UpperCamelCase					)
        _UpperCAmelCase           =   self.dummy_sample
        _UpperCAmelCase           =   0.1 * sample
        _UpperCAmelCase           =   [residual + 0.2, residual + 0.15, residual + 0.10]

        for scheduler_class in self.scheduler_classes:
           _UpperCAmelCase           =   self.get_scheduler_config()
           _UpperCAmelCase           =   scheduler_class(**_UpperCamelCase					)
           scheduler.set_timesteps(_UpperCamelCase					)

           # copy over dummy past residuals (must be after setting timesteps)
           _UpperCAmelCase           =   dummy_past_residuals[: scheduler.config.solver_order]

           with tempfile.TemporaryDirectory() as tmpdirname:
              scheduler.save_config(_UpperCamelCase					)
              _UpperCAmelCase           =   scheduler_class.from_pretrained(_UpperCamelCase					)
              # copy over dummy past residuals
              new_scheduler.set_timesteps(_UpperCamelCase					)

              # copy over dummy past residual (must be after setting timesteps)
              _UpperCAmelCase           =   dummy_past_residuals[: new_scheduler.config.solver_order]

           _UpperCAmelCase           =   scheduler.step(_UpperCamelCase				,							_UpperCamelCase				,							_UpperCamelCase				,							**_UpperCamelCase					).prev_sample
           _UpperCAmelCase           =   new_scheduler.step(_UpperCamelCase				,							_UpperCamelCase				,							_UpperCamelCase				,							**_UpperCamelCase					).prev_sample

           assert torch.sum(torch.abs(output - new_output					)					) < 1e-5, "Scheduler outputs are not identical"





     def 		UpperCamelCase(     self				,							_UpperCamelCase=None				,							**_UpperCamelCase					):
        if scheduler is None:
           _UpperCAmelCase           =   self.scheduler_classes[0]
           _UpperCAmelCase           =   self.get_scheduler_config(**_UpperCamelCase					)
           _UpperCAmelCase           =   scheduler_class(**_UpperCamelCase					)

        _UpperCAmelCase           =   self.scheduler_classes[0]
        _UpperCAmelCase           =   self.get_scheduler_config(**_UpperCamelCase					)
        _UpperCAmelCase           =   scheduler_class(**_UpperCamelCase					)

        _UpperCAmelCase           =   10
        _UpperCAmelCase           =   self.dummy_model()
        _UpperCAmelCase           =   self.dummy_sample_deter
        scheduler.set_timesteps(_UpperCamelCase					)

        for i, t in enumerate(scheduler.timesteps					):
           _UpperCAmelCase           =   model(_UpperCamelCase				,							_UpperCamelCase					)
           _UpperCAmelCase           =   scheduler.step(_UpperCamelCase				,							_UpperCamelCase				,							_UpperCamelCase					).prev_sample

        return sample





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase           =   dict(self.forward_default_kwargs					)

        _UpperCAmelCase           =   kwargs.pop('''num_inference_steps'''				,							_UpperCamelCase					)

        for scheduler_class in self.scheduler_classes:
           _UpperCAmelCase           =   self.get_scheduler_config()
           _UpperCAmelCase           =   scheduler_class(**_UpperCamelCase					)

           _UpperCAmelCase           =   self.dummy_sample
           _UpperCAmelCase           =   0.1 * sample

           if num_inference_steps is not None and hasattr(_UpperCamelCase				,							'''set_timesteps'''					):
              scheduler.set_timesteps(_UpperCamelCase					)
           elif num_inference_steps is not None and not hasattr(_UpperCamelCase				,							'''set_timesteps'''					):
              _UpperCAmelCase           =   num_inference_steps

           # copy over dummy past residuals (must be done after set_timesteps)
           _UpperCAmelCase           =   [residual + 0.2, residual + 0.15, residual + 0.10]
           _UpperCAmelCase           =   dummy_past_residuals[: scheduler.config.solver_order]

           _UpperCAmelCase           =   scheduler.timesteps[5]
           _UpperCAmelCase           =   scheduler.timesteps[6]

           _UpperCAmelCase           =   scheduler.step(_UpperCamelCase				,							_UpperCamelCase				,							_UpperCamelCase				,							**_UpperCamelCase					).prev_sample
           _UpperCAmelCase           =   scheduler.step(_UpperCamelCase				,							_UpperCamelCase				,							_UpperCamelCase				,							**_UpperCamelCase					).prev_sample

           self.assertEqual(output_a.shape				,							sample.shape					)
           self.assertEqual(output_a.shape				,							output_a.shape					)





     def 		UpperCamelCase(     self					):
        # make sure that iterating over schedulers with same config names gives same results
        # for defaults
        _UpperCAmelCase           =   UniPCMultistepScheduler(**self.get_scheduler_config()					)
        _UpperCAmelCase           =   self.full_loop(scheduler=_UpperCamelCase					)
        _UpperCAmelCase           =   torch.mean(torch.abs(_UpperCamelCase					)					)

        assert abs(result_mean.item() - 0.2464					) < 1e-3

        _UpperCAmelCase           =   DPMSolverSinglestepScheduler.from_config(scheduler.config					)
        _UpperCAmelCase           =   DEISMultistepScheduler.from_config(scheduler.config					)
        _UpperCAmelCase           =   DPMSolverMultistepScheduler.from_config(scheduler.config					)
        _UpperCAmelCase           =   UniPCMultistepScheduler.from_config(scheduler.config					)

        _UpperCAmelCase           =   self.full_loop(scheduler=_UpperCamelCase					)
        _UpperCAmelCase           =   torch.mean(torch.abs(_UpperCamelCase					)					)

        assert abs(result_mean.item() - 0.2464					) < 1e-3





     def 		UpperCamelCase(     self					):
        for timesteps in [25, 50, 100, 999, 1000]:
           self.check_over_configs(num_train_timesteps=_UpperCamelCase					)





     def 		UpperCamelCase(     self					):
        self.check_over_configs(thresholding=_UpperCamelCase					)
        for order in [1, 2, 3]:
           for solver_type in ["bh1", "bh2"]:
              for threshold in [0.5, 1.0, 2.0]:
                 for prediction_type in ["epsilon", "sample"]:
                    self.check_over_configs(
                        thresholding=_UpperCamelCase				,							prediction_type=_UpperCamelCase				,							sample_max_value=_UpperCamelCase				,							solver_order=_UpperCamelCase				,							solver_type=_UpperCamelCase				,							)





     def 		UpperCamelCase(     self					):
        for prediction_type in ["epsilon", "v_prediction"]:
           self.check_over_configs(prediction_type=_UpperCamelCase					)





     def 		UpperCamelCase(     self					):
        for solver_type in ["bh1", "bh2"]:
           for order in [1, 2, 3]:
              for prediction_type in ["epsilon", "sample"]:
                 self.check_over_configs(
                     solver_order=_UpperCamelCase				,							solver_type=_UpperCamelCase				,							prediction_type=_UpperCamelCase				,							)
                 _UpperCAmelCase           =   self.full_loop(
                     solver_order=_UpperCamelCase				,							solver_type=_UpperCamelCase				,							prediction_type=_UpperCamelCase				,							)
                 assert not torch.isnan(_UpperCamelCase					).any(), "Samples have nan numbers"





     def 		UpperCamelCase(     self					):
        self.check_over_configs(lower_order_final=_UpperCamelCase					)
        self.check_over_configs(lower_order_final=_UpperCamelCase					)





     def 		UpperCamelCase(     self					):
        for num_inference_steps in [1, 2, 3, 5, 10, 50, 100, 999, 1000]:
           self.check_over_forward(num_inference_steps=_UpperCamelCase				,							time_step=0					)





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase           =   self.full_loop()
        _UpperCAmelCase           =   torch.mean(torch.abs(_UpperCamelCase					)					)

        assert abs(result_mean.item() - 0.2464					) < 1e-3





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase           =   self.full_loop(prediction_type='''v_prediction'''					)
        _UpperCAmelCase           =   torch.mean(torch.abs(_UpperCamelCase					)					)

        assert abs(result_mean.item() - 0.1014					) < 1e-3





     def 		UpperCamelCase(     self					):
        _UpperCAmelCase           =   self.scheduler_classes[0]
        _UpperCAmelCase           =   self.get_scheduler_config(thresholding=_UpperCamelCase				,							dynamic_thresholding_ratio=0					)
        _UpperCAmelCase           =   scheduler_class(**_UpperCamelCase					)

        _UpperCAmelCase           =   10
        _UpperCAmelCase           =   self.dummy_model()
        _UpperCAmelCase           =   self.dummy_sample_deter.half()
        scheduler.set_timesteps(_UpperCamelCase					)

        for i, t in enumerate(scheduler.timesteps					):
           _UpperCAmelCase           =   model(_UpperCamelCase				,							_UpperCamelCase					)
           _UpperCAmelCase           =   scheduler.step(_UpperCamelCase				,							_UpperCamelCase				,							_UpperCamelCase					).prev_sample

        assert sample.dtype == torch.floataa





     def 		UpperCamelCase(     self				,							**_UpperCamelCase					):
        for scheduler_class in self.scheduler_classes:
           _UpperCAmelCase           =   self.get_scheduler_config(**_UpperCamelCase					)
           _UpperCAmelCase           =   scheduler_class(**_UpperCamelCase					)

           scheduler.set_timesteps(scheduler.config.num_train_timesteps					)
           assert len(scheduler.timesteps.unique()					) == scheduler.num_inference_steps
"""simple docstring"""


from math import sqrt





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   bool:




						'''simple docstring'''



						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							) and (
						    number >= 0
						), "'number' must been an int and positive"

						lowerCamelCase__   =True

						# 0 and 1 are none primes.
						if number <= 1:
												lowerCamelCase__   =False

						for divisor in range(2  ,       int(round(sqrt(__lowerCAmelCase							)							)							) + 1							):
												# if 'number' divisible by 'divisor' then sets 'status'
												# of false and break up the loop.
												if number % divisor == 0:
																		lowerCamelCase__   =False
																		break

    # precondition
						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							), "'status' must been from type bool"

						return status





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   List[str]:




						'''simple docstring'''



						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							) and (n > 2), "'N' must been an int and > 2"

						# beginList: contains all natural numbers from 2 up to N
						lowerCamelCase__   =list(range(2  ,       n + 1							)							)

						lowerCamelCase__   =[]  # this list will be returns.

						# actual sieve of erathostenes
						for i in range(len(__lowerCAmelCase							)							):
												for j in range(i + 1  ,       len(__lowerCAmelCase							)							):
																		if (begin_list[i] != 0) and (begin_list[j] % begin_list[i] == 0):
																								lowerCamelCase__   =0

    # filters actual prime numbers.
						lowerCamelCase__   =[x for x in begin_list if x != 0]

						# precondition
						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							), "'ans' must been from type list"

						return ans





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   Optional[int]:




						'''simple docstring'''



						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							) and (n > 2), "'N' must been an int and > 2"

						lowerCamelCase__   =[]

						# iterates over all numbers between 2 up to N+1
						# if a number is prime then appends to list 'ans'
						for number in range(2  ,       n + 1							):
												if is_prime(__lowerCAmelCase							):
																		ans.append(__lowerCAmelCase							)

    # precondition
						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							), "'ans' must been from type list"

						return ans





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   Union[str, Any]:




						'''simple docstring'''



						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							) and number >= 0, "'number' must been an int and >= 0"

						lowerCamelCase__   =[]  # this list will be returns of the function.

						# potential prime number factors.

						lowerCamelCase__   =2

						lowerCamelCase__   =number

						if number == 0 or number == 1:
												ans.append(__lowerCAmelCase							)

						# if 'number' not prime then builds the prime factorization of 'number'
						elif not is_prime(__lowerCAmelCase							):
												while quotient != 1:
																		if is_prime(__lowerCAmelCase							) and (quotient % factor == 0):
																								ans.append(__lowerCAmelCase							)
																								quotient /= factor
																		else:
																								factor += 1

						else:
												ans.append(__lowerCAmelCase							)

						# precondition
						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							), "'ans' must been from type list"

						return ans





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   Optional[int]:




						'''simple docstring'''



						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							) and (
						    number >= 0
						), "'number' bust been an int and >= 0"

						lowerCamelCase__   =0

						# prime factorization of 'number'
						lowerCamelCase__   =prime_factorization(__lowerCAmelCase							)

						lowerCamelCase__   =max(__lowerCAmelCase							)

						# precondition
						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							), "'ans' must been from type int"

						return ans





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   List[Any]:




						'''simple docstring'''



						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							) and (
						    number >= 0
						), "'number' bust been an int and >= 0"

						lowerCamelCase__   =0

						# prime factorization of 'number'
						lowerCamelCase__   =prime_factorization(__lowerCAmelCase							)

						lowerCamelCase__   =min(__lowerCAmelCase							)

						# precondition
						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							), "'ans' must been from type int"

						return ans





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   Union[str, Any]:




						'''simple docstring'''



						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							), "'number' must been an int"
						assert isinstance(number % 2 == 0  ,       __lowerCAmelCase							), "compare bust been from type bool"

						return number % 2 == 0





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   List[Any]:




						'''simple docstring'''



						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							), "'number' must been an int"
						assert isinstance(number % 2 != 0  ,       __lowerCAmelCase							), "compare bust been from type bool"

						return number % 2 != 0





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   int:




						'''simple docstring'''



						assert (
						    isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							) and (number > 2) and is_even(__lowerCAmelCase							)
						), "'number' must been an int, even and > 2"

						lowerCamelCase__   =[]  # this list will returned

						# creates a list of prime numbers between 2 up to 'number'
						lowerCamelCase__   =get_prime_numbers(__lowerCAmelCase							)
						lowerCamelCase__   =len(__lowerCAmelCase							)

						# run variable for while-loops.
						lowerCamelCase__   =0
						lowerCamelCase__   =None

						# exit variable. for break up the loops
						lowerCamelCase__   =True

						while i < len_pn and loop:
												lowerCamelCase__   =i + 1

												while j < len_pn and loop:
																		if prime_numbers[i] + prime_numbers[j] == number:
																								lowerCamelCase__   =False
																								ans.append(prime_numbers[i]							)
																								ans.append(prime_numbers[j]							)

																		j += 1

												i += 1

						# precondition
						assert (
						    isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							)
						    and (len(__lowerCAmelCase							) == 2)
						    and (ans[0] + ans[1] == number)
						    and is_prime(ans[0]							)
						    and is_prime(ans[1]							)
						), "'ans' must contains two primes. And sum of elements must been eq 'number'"

						return ans





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase							)				->   Tuple:




						'''simple docstring'''



						assert (
						    isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							)
						    and isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							)
						    and (numbera >= 0)
						    and (numbera >= 0)
						), "'number1' and 'number2' must been positive integer."

						lowerCamelCase__   =0

						while numbera != 0:
												lowerCamelCase__   =numbera % numbera
												lowerCamelCase__   =numbera
												lowerCamelCase__   =rest

						# precondition
						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							) and (
						    numbera >= 0
						), "'number' must been from type int and positive"

						return numbera





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase							)				->   Union[str, Any]:




						'''simple docstring'''



						assert (
						    isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							)
						    and isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							)
						    and (numbera >= 1)
						    and (numbera >= 1)
						), "'number1' and 'number2' must been positive integer."

						lowerCamelCase__   =1  # actual answer that will be return.

						# for kgV (x,1)
						if numbera > 1 and numbera > 1:
												# builds the prime factorization of 'number1' and 'number2'
												lowerCamelCase__   =prime_factorization(__lowerCAmelCase							)
												lowerCamelCase__   =prime_factorization(__lowerCAmelCase							)

						elif numbera == 1 or numbera == 1:
												lowerCamelCase__   =[]
												lowerCamelCase__   =[]
												lowerCamelCase__   =max(__lowerCAmelCase  ,       __lowerCAmelCase							)

						lowerCamelCase__   =0
						lowerCamelCase__   =0

						lowerCamelCase__   =[]  # captured numbers int both 'primeFac1' and 'primeFac2'

						# iterates through primeFac1
						for n in prime_fac_a:
												if n not in done:
																		if n in prime_fac_a:
																								lowerCamelCase__   =prime_fac_a.count(__lowerCAmelCase							)
																								lowerCamelCase__   =prime_fac_a.count(__lowerCAmelCase							)

																								for _ in range(max(__lowerCAmelCase  ,       __lowerCAmelCase							)							):
																														ans *= n

																		else:
																								lowerCamelCase__   =prime_fac_a.count(__lowerCAmelCase							)

																								for _ in range(__lowerCAmelCase							):
																														ans *= n

																		done.append(__lowerCAmelCase							)

    # iterates through primeFac2
						for n in prime_fac_a:
												if n not in done:
																		lowerCamelCase__   =prime_fac_a.count(__lowerCAmelCase							)

																		for _ in range(__lowerCAmelCase							):
																								ans *= n

																		done.append(__lowerCAmelCase							)

    # precondition
						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							) and (
						    ans >= 0
						), "'ans' must been from type int and positive"

						return ans





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   Optional[Any]:




						'''simple docstring'''



						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							) and (n >= 0), "'number' must been a positive int"

						lowerCamelCase__   =0
						lowerCamelCase__   =2  # this variable holds the answer

						while index < n:
												index += 1

												ans += 1  # counts to the next number

												# if ans not prime then
												# runs to the next prime number.
												while not is_prime(__lowerCAmelCase							):
																		ans += 1

    # precondition
						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							) and is_prime(
						    __lowerCAmelCase							), "'ans' must been a prime number and from type int"

						return ans





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase							)				->   int:




						'''simple docstring'''



						assert (
						    is_prime(__lowerCAmelCase							) and is_prime(__lowerCAmelCase							) and (p_number_a < p_number_a)
						), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

						lowerCamelCase__   =p_number_a + 1  # jump to the next number

						lowerCamelCase__   =[]  # this list will be returns.

						# if number is not prime then
						# fetch the next prime number.
						while not is_prime(__lowerCAmelCase							):
												number += 1

						while number < p_number_a:
												ans.append(__lowerCAmelCase							)

												number += 1

												# fetch the next prime number.
												while not is_prime(__lowerCAmelCase							):
																		number += 1

    # precondition
						assert (
						    isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							)
						    and ans[0] != p_number_a
						    and ans[len(__lowerCAmelCase							) - 1] != p_number_a
						), "'ans' must been a list without the arguments"

						# 'ans' contains not 'pNumber1' and 'pNumber2' !
						return ans





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   int:




						'''simple docstring'''



						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							) and (n >= 1), "'n' must been int and >= 1"

						lowerCamelCase__   =[]  # will be returned.

						for divisor in range(1  ,       n + 1							):
												if n % divisor == 0:
																		ans.append(__lowerCAmelCase							)

    # precondition
						assert ans[0] == 1 and ans[len(__lowerCAmelCase							) - 1] == n, "Error in function getDivisiors(...)"

						return ans





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   Union[str, Any]:




						'''simple docstring'''



						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							) and (
						    number > 1
						), "'number' must been an int and >= 1"

						lowerCamelCase__   =get_divisors(__lowerCAmelCase							)

						# precondition
						assert (
						    isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							)
						    and (divisors[0] == 1)
						    and (divisors[len(__lowerCAmelCase							) - 1] == number)
						), "Error in help-function getDivisiors(...)"

						# summed all divisors up to 'number' (exclusive), hence [:-1]
						return sum(divisors[:-1]							) == number





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase							)				->   Dict:




						'''simple docstring'''



						assert (
						    isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							)
						    and isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							)
						    and (denominator != 0)
						), "The arguments must been from type int and 'denominator' != 0"

						# build the greatest common divisor of numerator and denominator.
						lowerCamelCase__   =gcd(abs(__lowerCAmelCase							)  ,       abs(__lowerCAmelCase							)							)

						# precondition
						assert (
						    isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							)
						    and (numerator % gcd_of_fraction == 0)
						    and (denominator % gcd_of_fraction == 0)
						), "Error in function gcd(...,...)"

						return (numerator // gcd_of_fraction, denominator // gcd_of_fraction)





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   List[Any]:




						'''simple docstring'''



						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							) and (n >= 0), "'n' must been a int and >= 0"

						lowerCamelCase__   =1  # this will be return.

						for factor in range(1  ,       n + 1							):
												ans *= factor

						return ans





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   Tuple:




						'''simple docstring'''



						assert isinstance(__lowerCAmelCase  ,       __lowerCAmelCase							) and (n >= 0), "'n' must been an int and >= 0"

						lowerCamelCase__   =0
						lowerCamelCase__   =1
						lowerCamelCase__   =1  # this will be return

						for _ in range(n - 1							):
												lowerCamelCase__   =ans
												ans += fiba
												lowerCamelCase__   =tmp

						return ans


